A Bilinear Algorithm for Optimizing a Linear Function over the Efficient Set of a Multiple Objective Linear Programming Problem
The problem Q of optimizing a linear function over the efficient set of a multiple objective linear program serves several useful purposes in multiple criteria decision making. However, Q is in itself a difficult global optimization problem, whose local optima, frequently large in number, need not b...
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| Vydané v: | Journal of global optimization Ročník 31; číslo 1; s. 1 - 16 |
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| Médium: | Journal Article |
| Jazyk: | English |
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Springer Nature B.V
01.01.2005
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| ISSN: | 0925-5001, 1573-2916 |
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| Abstract | The problem Q of optimizing a linear function over the efficient set of a multiple objective linear program serves several useful purposes in multiple criteria decision making. However, Q is in itself a difficult global optimization problem, whose local optima, frequently large in number, need not be globally optimal. Indeed, this is due to the fact that the feasible region of Q is, in general, a nonconvex set. In this paper we present a monotonically increasing algorithm that finds an exact, globally-optimal solution for Q. Our approach does not require any hypothesis on the boundedness of neither the efficient set EP nor the optimal objective value. The proposed algorithm relies on a simplified disjoint bilinear program that can be solved through the use of well-known specifically designed methods within nonconvex optimization. The algorithm has been implemented in C and preliminary numerical results are reported. [PUBLICATION ABSTRACT] |
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| AbstractList | The problem Q of optimizing a linear function over the efficient set of a multiple objective linear program serves several useful purposes in multiple criteria decision making. However, Q is in itself a difficult global optimization problem, whose local optima, frequently large in number, need not be globally optimal. Indeed, this is due to the fact that the feasible region of Q is, in general, a nonconvex set. In this paper we present a monotonically increasing algorithm that finds an exact, globally-optimal solution for Q. Our approach does not require any hypothesis on the boundedness of neither the efficient set EP nor the optimal objective value. The proposed algorithm relies on a simplified disjoint bilinear program that can be solved through the use of well-known specifically designed methods within nonconvex optimization. The algorithm has been implemented in C and preliminary numerical results are reported. [PUBLICATION ABSTRACT] |
| Author | Jorge, Jesús M. |
| Author_xml | – sequence: 1 givenname: Jesús M. surname: Jorge fullname: Jorge, Jesús M. |
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| CitedBy_id | crossref_primary_10_1016_j_cor_2018_10_009 crossref_primary_10_1111_itor_12627 crossref_primary_10_1007_s10957_008_9467_2 crossref_primary_10_4000_etudescaribeennes_16333 crossref_primary_10_1080_10556788_2024_2380688 crossref_primary_10_1111_itor_13202 crossref_primary_10_1016_j_ejor_2008_02_005 crossref_primary_10_1016_j_ejor_2008_10_003 crossref_primary_10_1111_itor_13547 crossref_primary_10_1007_s10479_020_03820_4 crossref_primary_10_1080_02331930903500290 crossref_primary_10_18187_pjsor_v18i1_3261 |
| Cites_doi | 10.1007/BFb0121041 10.1016/0167-6377(91)90026-L 10.1007/BF00940077 10.1016/0377-2217(88)90257-3 10.1016/0022-247X(75)90189-4 10.1007/978-3-662-03199-5 10.1002/1520-6750(199302)40:1<103::AID-NAV3220400107>3.0.CO;2-A 10.1007/BF02196590 10.1007/BF01100242 10.1007/PL00011428 10.1007/BF00120667 10.1515/9781400873173 10.1016/S0167-6377(02)00216-X 10.1016/0022-247X(84)90269-5 10.1287/opre.48.1.65.12449 10.1007/s101070050072 10.1007/BF01580111 10.1007/BF02192023 10.1007/BF02207641 10.1007/BF01584543 10.1007/BF01580453 |
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| DOI | 10.1007/s10898-003-3784-7 |
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| Title | A Bilinear Algorithm for Optimizing a Linear Function over the Efficient Set of a Multiple Objective Linear Programming Problem |
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